English

Regge calculus in the canonical form

General Relativity and Quantum Cosmology 2015-06-25 v1

Abstract

(3+1) (continuous time) Regge calculus is reduced to Hamiltonian form. The constraints are classified, classical and quantum consequences are discussed. As basic variables connection matrices and antisymmetric area tensors are used supplemented with appropriate bilinear constraints. In these variables the action can be made quasipolinomial with arcsin\arcsin as the only deviation from polinomiality. In comparison with analogous formalism in the continuum theory classification of constraints changes: some of them disappear, the part of I class constraints including Hamiltonian one become II class (and vice versa, some new constraints arise and some II class constraints become I class). As a result, the number of the degrees of freedom coincides with the number of links in 3-dimensional leaf of foliation. Moreover, in empty space classical dynamics is trivial: the scale of timelike links become zero and spacelike links are constant.

Keywords

Cite

@article{arxiv.gr-qc/9310004,
  title  = {Regge calculus in the canonical form},
  author = {V. Khatsymovsky},
  journal= {arXiv preprint arXiv:gr-qc/9310004},
  year   = {2015}
}

Comments

24 pages,Plain LaTeX,BINP 93-42

R2 v1 2026-07-22T12:48:35.253Z